School of Mathematics and Statistics

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    Disconjugacy, conjugacy and oscillation criteria for continuous and discrete linear hamiltonian systems
    (University of Hyderabad, 1989-01-20) Sowjanya Kumari, I. ; Umamaheswaram, S.
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    Focal boundary value problems for ordinary differential equations
    (University of Hyderabad, 1989-02-26) Venkata Rama, Modali ; Umamaheswaram, S.
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    On object representation schemes
    (University of Hyderabad, 1989-07-24) Lavakusha, B. ; Pujari, A.K.
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    On an error term related to the Jordan totient function J < inf > k < /inf > (n)
    ( 1990-01-01) Adhikari, Sukumar Das ; Sankaranarayanan, A.
    We investigate the error terms Ek(x)= ∑ n≤xJk(n)- xk+1 (k+1)ζ(k+1) for k≥2, where Jk(n) = nkΠp|n(1 - 1 pk) for k ≥ 1. For k ≥ 2, we prove ∑ n≤xEk(n)∼ xk+1 2(k+1)ζ(k+1). Also, lim inf n→∞ Ek(x) xk≤ D ζ(k+1), where D = .7159 when k = 2, .6063 when k ≥ 3. On the other hand, even though lim inf n→∞ Ek(x) xk≤- 1 2ζ(k+1), Ek(n) > 0 for integers n sufficiently large. © 1990.
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    On the frequency of Titchmarsh's phenomenon for ζ(s)-VIII
    ( 1992-04-01) Balasubramanian, R. ; Ramachandra, K. ; Sankaranarayanan, A.
    For suitable functions H = H(T) the maximum of |(ζ(σ + it)) z | taken over T≤t≤T + H is studied. For fixed σ(1/2≤σ≤l) and fixed complex constants z "expected lower bounds" for the maximum are established. © 1992 Indian Academy of Sciences.
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    On some theorems of littlewood and selberg, I
    ( 1993-01-01) Ramachandra, K. ; Sankaranarayanan, A.
    Assuming the Riemann hypothesis, we prove [formula] and [formula] with economical constants D1 = 0.46657029869824… and D2 = 3.51588780218300… . © 1993 Academic Press Inc.
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    Mean-value theorem of the riemann zeta-function over short intervals
    ( 1993-01-01) Sankaranarayanan, A. ; Srinivas, K.
    Let s = σ + it. Then, on the assumption of Riemann Hypothesis, we prove the Mean-Value Theorem for the square of the Riemann zeta-function over shorter intervals for 1/2 + A1/log log T ≤ σ ≤ 1 - δ. Here A1 is a large positive constant, δ is a small positive constant, and T ≤ t ≤ T + H where H depends on T satisfying H ≤ T. © 1993 Academic Press Inc.
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    Lexisearch approach to some combinatorial programming problems
    (University of Hyderabad, 1997-01-10) Ramesh, M. ; Narahari Pandit, S.N.
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    Sets of periods of continuous self maps on some metric spaces
    (University of Hyderabad, 1997-11-19) Saradhi, P.V.S.P. ; Kannan, V.
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    On a method of Balasubramanian and Ramachandra (on the abelian group problem)
    ( 1997-12-01) Sankaranarayanan, A. ; Srinivas, K.
    Let an denote the number of non-isomorphic abelian groups of order n. We consider A(x) = Σn≤x an = Σj=110 Cjx1/j + E(x) where E(x) is the error term. We study E(x) through the general method of Balasubramanian and Ramachandra.
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    Geometric and analytic studies of some integrable systems
    (University of Hyderabad, 1998-12-31) Subbulakshmi, S. ; Sitaramayya, M.
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    On Liapunov-Type Inequality for Third-Order Differential Equations
    ( 1999-05-15) Parhi, N. ; Panigrahi, S.
    In this paper, a Liapunov-type inequality has been derived for a class of third-order differential equations of the form,y‴+pty=0,wherepis a real-valued continuous function on [0,∞). The nature of the distance between consecutive two zeros or three zeros has been studied with the help of the inequality. © 1999 Academic Press.
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    Goldbach problem in polynomial values
    ( 1999-06-01) Sankaranarayanan, A.
    An even integer n ≥ 6 is called a Goldbach number if it is the sum of two odd primes. The Goldbach conjecture says that every even number n ≤ 6 is a Goldbach number. In this paper, we study the mean-square upper bound of the error term related to the Goldbach problem, in polynomial values over short intervals, uniformly with respect to the height of a polynomial of fixed degree. © 1999 Springer.
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    Liapunov-type inequality for delay-differential equations of third order
    ( 2002-09-12) Parhi, N. ; Panigrahi, S.
    A Liapunov-type inequality for a class of third order delay-differential equations is derived.
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    Distinguished representatitions for GL(n)
    (University of Hyderabad, 2002-09-30) Anandavardhanan, U.K. ; Tandon, Rajat
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    Disfocality and Liapunov-type inequalities for third-order equations
    ( 2003-02-01) Parhi, N. ; Panigrahi, S.
    The concept of disfocality is introduced for third-order differential equations y ‴ + p(t)y = 0. This helps to improve the Liapunov inequality when y(t) is a solution of (*) with y(a) = 0 = y′(a), y(b) = 0 = y′(b), and y(t) ≠ 0, t ε (a, b). If y(t) is a solution of (*) with y(t 1) = 0 = y (t 2) = y(t 3) = y(t 4) (t 1 < t 2 < t 3 < t 4) and y(t) ≠ 0 for t ε ∪ 3i=1(t i,t i+1), then the lower bound for (t 4-t 1) is obtained. A new criteria is obtained for disconjugacy of (*) in [a, b]. © 2003 Elsevier Science Ltd. All rights reserved.
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    Bayesian integrated functional analysis of microarray data
    ( 2004-11-22) Bhattacharjee, Madhuchhanda ; Pritchard, Colin C. ; Nelson, Peter S. ; Arjas, Elja
    Motivation: The statistical analysis of microarray data usually proceeds in a sequential manner, with the output of the previous step always serving as the input of the next one. However, the methods currently used in such analyses do not properly account for the fact that the intermediate results may not always be correct, then leading to cumulating error in the inferences drawn based on such steps. Results: Here we show that, by an application of hierarchical Bayesian methodology, this sequential procedure can be replaced by a single joint analysis, while systematically accounting for the uncertainties in this process. Moreover, we can also integrate relevant functional information available from databases into such an analysis, thereby increasing the reliability of the biological conclusions that are drawn. We illustrate these points by analysing real data and by showing that the genes can be divided into categories of interest, with the defining characteristic depending on the biological question that is considered. We contend that the proposed method has advantages at two levels. First, there are gains in the statistical and biological results from the analysis of this particular dataset. Second, it opens up new possibilities in analysing microarray data in general. © Oxford University Press 2004; all rights reserved.
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    Bayesian association-based fine mapping in small chromosomal segments
    ( 2005-01-01) Sillanpää, Mikko J. ; Bhattacharjee, Madhuchhanda
    A Bayesian method for fine mapping is presented, which deals with multiallelic markers (with two or more alleles), unknown phase, missing data, multiple causal variants, and both continuous and binary phenotypes. We consider small chromosomal segments spanned by a dense set of closely linked markers and putative genes only at marker points. In the phenotypic model, locus-specific indicator variables are used to control inclusion in or exclusion from marker contributions. To account for covariance between consecutive loci and to control fluctuations in association signals along a candidate region we introduce a joint prior for the indicators that depends on genetic or physical map distances. The potential of the method, including posterior estimation of trait-associated loci, their effects, linkage disequilibrium pattern due to close linkage of loci, and the age of a causal variant (time to most recent common ancestor), is illustrated with the well-known cystic fibrosis and Friedreich ataxia data sets by assuming that haplotypes were not available. In addition, simulation analysis with large genetic distances is shown. Estimation of model parameters is based on Markov chain Monte Carlo (MCMC) sampling and is implemented using WinBUGS. The model specification code is freely available for research purposes from http://www.rni.helsinki.fi/~mjs/.